choose.h

/** * \file choose.h * \brief \todo brief description * * Copyright 2006 Nathan Hurst <njh@mail.csse.monash.edu.au> * * This library is free software; you can redistribute it and/or * modify it either under the terms of the GNU Lesser General Public * License version 2.1 as published by the Free Software Foundation * (the "LGPL") or, at your option, under the terms of the Mozilla * Public License Version 1.1 (the "MPL"). If you do not alter this * notice, a recipient may use your version of this file under either * the MPL or the LGPL. * * You should have received a copy of the LGPL along with this library * in the file COPYING-LGPL-2.1; if not, write to the Free Software * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA * You should have received a copy of the MPL along with this library * in the file COPYING-MPL-1.1 * * The contents of this file are subject to the Mozilla Public License * Version 1.1 (the "License"); you may not use this file except in * compliance with the License. You may obtain a copy of the License at * http://www.mozilla.org/MPL/ * * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY * OF ANY KIND, either express or implied. See the LGPL or the MPL for * the specific language governing rights and limitations. * */#ifndef _CHOOSE_H#define _CHOOSE_H#include <vector>// XXX: Can we keep only the left terms easily? // this would more than halve the array// row index becomes n2 = n/2, row2 = n2*(n2+1)/2, row = row2*2+(n&1)?n2:0// we could also leave off the onestemplate <typename T>
T choose(unsigned n, unsigned k) {
static std::vector<T> pascals_triangle;
staticunsigned rows_done = 0;
// indexing is (0,0,), (1,0), (1,1), (2, 0)...// to get (i, j) i*(i+1)/2 + jif(/*k < 0 ||*/ k > n) return 0;
if(rows_done <= n) {// we haven't got there yetif(rows_done == 0) {
pascals_triangle.push_back(1);
rows_done = 1;
}
while(rows_done <= n) {
unsigned p = pascals_triangle.size() - rows_done;
pascals_triangle.push_back(1);
for(unsigned i = 0; i < rows_done-1; i++) {
pascals_triangle.push_back(pascals_triangle[p]
+ pascals_triangle[p+1]);
p++;
}
pascals_triangle.push_back(1);
rows_done ++;
}
}
unsigned row = (n*(n+1))/2;
return pascals_triangle[row+k];
}
// Is it faster to store them or compute them on demand?/*template <typename T>T choose(unsigned n, unsigned k) { T r = 1; for(unsigned i = 1; i <= k; i++) r = (r*(n-k+i))/i; return r; }*/#endif/* Local Variables: mode:c++ c-file-style:"stroustrup" c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) indent-tabs-mode:nil fill-column:99 End:*/// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :